You may have some failed caps on the processor board, I would also check the voltage regulators as well.
The glue that is used to hold the regulators down to the board is very well known to dry out and become conductive/corrosive and cause them to stop working.
Many times carefully lifting them from the board will bring the radio/display back to life.
Also check anywhere that the glue is, carefully remove the glue, and look for corrosion on any leads that the glue has been on.
I have seen it eat through tiny traces on the CPU board....on one radio it had eaten away one of the leads on the broadband output transformer at the back of the radio.
As for getting the radio to lock on 12 meters, Look at Rogerbirds page here:
http://www.cbtricks.com/rogerbird/2510/24mhz.html
I have used method #2 before on radios that did not want to lock on 12 meters and it solved the problem.
As I have said many times before, the 2510/2600/2830/Lincoln radios are a good radio, but they are getting very long in the tooth and many are showing there age.
I still have a 2510/w Chipswitch, a 2600 that is still factory on ten meters, and one of the last production runs of the Lincoln that used the MRF 497 from the factory before they went to the MRF 455.
All have been recapped and I have managed to "pick" most of the glue off of them with no problems so far.
The Lincoln at the moment is my daily driver radio in my pickup, it has been recapped, has a channel guard filter in it, upgraded NB and AM detector diodes and a Panther Electronics 10M SSB kit in it.
Remember, these radios are late 1980`s technology, parts are unable to be sourced anymore, the LCD displays are getting old and are prone to "leaking" around the edges, ChipSwitches are no longer being made, the Motorola MRF 477, MRF497 And the MRF 455 are also out of production.
Do Not exceed 10 watts carrier AM/FM and 25/30 watts SSB.
Yes both the 477, 497 and the 455 transistors will provide more output, but the radio was not designed for it.
I have heard guys claim to run 40 watts AM/FM from the 477/497 and 75 watts out of the lincoln with the 455 in them......not for long.
The 455 itself will do /60/70 watts but the radio will not support it.
Ask weazle 66, he has probably replaced more finals in this series of radios than anyone on the planet.
73
Jeff